Analysing the multidimensional wave climate with self organizing maps

The term “wave climate” usually refers to the statistical distribution of several oceanographical geophysical variables. Components of the wave climate are variables such as wind velocity, W, wind direction, θW, significant wave height, Hs, peak period, Tp, and mean wave direction, θ. Usually, the classical analysis of the long-term distribution of wave climate is addressed using just one variable (f.i., long-term distribution of significant wave height) or at most bidimensionally (f.i., the bidimensional distribution of Hs and Tp). It is clear that the joint probability distribution of these five variables (Hs, Tp, θ, W, θW) is not easy to able to cope with. However, this problem is solved applying a non-linear clustering algorithm, namely the Self Organizing Maps (SOM), a neural network technique capable of classifying the high dimensional input reanalysis data in a low number of centroids (clusters) in an ordered sheet shape representation (Camus et al, 2007). The neurons are connected to adjacent elements by a neighbourhood relation. A multidimensional histogram of the sea state parameters is obtained allowing an easy further treatment of the classified sea states.

Figure 1 shows a 23x23 SOM applied to a particular site located in Villano, Galicia (Spain). In this case, the original data space has been projected into a toroid lattice being the data accommodated in a circular way. This toroid shape has been again projected into the plane for a better visualization, separating the centroids which are located together, the centroids located in the upper side of the sheet are joined with the centroids
located on the lower side of the sheet and with the lateral sides in the 3D-dimension. Each cell of the SOM represents a cluster defined by the five parameters employed in the classification. The significant wave height, the wave period and the wave direction are represented by the size, the colour intensity and the direction of the arrow; the pink arrow represents the wind vector. The background of each hexagon has been filled in a blue scale, function of the frequency of occurrence. As it can be seen in the figure, this classification technique is capable of extracting all the possible sea states and the transition between them. The magnitudes of the parameters which define the centroids vary smoothly from one cell to another. The most energetic sea states present W-WNW
directions (i=17, j=14). The higher amount of data is grouped in clusters with low energy sea states (i=6, j=11).

Figure 2 shows several SOMs for different locations along the northern coast of Spain. In this case, we are considering (Hs, Tp, θ) and a 10x10 SOM. In the presentation, the theoretical basis and some examples will show the ability of this methodology to describe the multidimensional wave climate.